My PhD thesis (keeping updated)

(If you spot any errors in the thesis, please contact me at puzhang0702@gmail.com, so that I can correct them. Thanks!)

Title: Theory of transformation optics and invisibility cloak design

Abstract:

Research on metamaterials has been growing ever since the first experimental realization of a double negative medium. The theory of transformation optics offers a perfect tool to exploit the vast possibilities of the constitutive parameters of metamaterials. A lot of fascinating optical devices have been identified, especially invisibility cloaks. The aim of this thesis is to contribute to the development of the basic theory of transformation optics, and use it to design invisibility cloaks for various applications. 

Background and the theory of transformation optics are introduced first. Formulas of transformed material parameters and transformed fields are thoroughly derived and detailed explanations are provided, so that the working knowledge of transformation optics can be acquired with minimal prerequisite mathematics. A proof of the form invariance of full Maxwell’s equations with sources is presented. Design procedure is then demonstrated by creating perfect invisibility cloaks. The introduction to the basic theory is followed by discussions of our published works. 

In the first application, a method of designing two-dimensional simplified cloaks of complex shapes is proposed to remove the singularity occurring in perfect cloaks. This intuitive and rather simple method is the first way to design two-dimensional simplified cloaks of shapes other than circular. Elliptical and bowtie shaped simplified cloaks are presented to verify the effectiveness of the method. Substantial scattering reduction is observed in both cases. 

Due to practical considerations, transformations continuous in the whole space must be the identity operation outside a certain volume, and thus they can only manipulate fields locally. Discontinuous transformations are naturally considered to break this limitation. We study the possible reflection from such a transformed medium due to a discontinuous transformation by introducing a new concept: inverse transformation optics. In this way, the reflection falls into the framework of transformation optics as well. Necessary and sufficient condition for no reflection is then derived as a special case. 

Unlike the invisibility realized by perfect cloaks, cloaking an object over a dielectric half-space has advantages in some particular applications. Starting from a perfect cloak, a half-space cloak is designed to achieve the invisibility in an air half-space over a dielectric ground. In our design, two matching strips embedded in the dielectric ground are used to induce proper reflection in the air half-space, so that the reflected field is the same as that from the bare dielectric ground. 

Cloaks obtained from singular transformations and even simplified models all have null principal values in their material parameters, making invisibility inherently a very narrowband effect. In contrast, a carpet cloak designed by only coordinate deformation does not have the narrowband limitation, and therefore can perform well in a broad spectrum. The invisibility accomplished by the carpet cloak is only with respect to EM waves in a half-space bounded by a perfect electric conductor, similar to the previous half-space cloak. In this part, we extend the original version of the carpet cloak to a general dielectric ground.

Link
https://docs.google.com/leaf?id=0BwhwtIdXtD2kYjZmMmU5YzMtNGUwYy00MDc1LWI0NmQtMjFmNTVkNDU2NjEy&sort=name&layout=list&num=50